The ark had already been removed from the temple and hidden by Gods direction. The ark and most of the other important temple items were not taken to Babylon.
Right now, I would say that Ron Wyat has the most likely discovery.
All the temple rites were 'types' or 'pictures' of what God had planed for the forgiveness of sin.
When on the day of atonement, the high priest splattered the blood of the sacifical lamb on the ark, it repersented Jesus as out high priest spilling His own on the Ark when He was crucified.
The lamb that was sacrificed had to be perfect in every way and spotless.
The high priest also had to be acceptable in Gods sight. It was not uncommon for a high priest to be struck dead when entering the 'holy of holies' or the part of the temple that the ark was located in. The high priest had a rope tied around his leg so that if he was struck dead, the other priests and temple workers could pull him out without being struck down themselves.
The 'picture' or 'type' represented by the temple worship was of a perfect sacrifice made by the high priest who alone was aceptable to God.
If a 'high priest' was unaceptable to God, he would lose his life simply by entering the 'holy of holies' or attempting to splatter the blood on the ark.
And how do we know this?
And .. they sewed little bells on the bottom of his clothing .. and when the bells stopped ringing, they knew to use the rope to pull the guy out of the temple - because he was dead.
Although I was always somewhat sketical of the books in the Apocrypha, it does say this in 2 Maccabees, chapter 2: note verses 4 and 5.
1: It is also found in the records, that Jeremy the prophet commanded them that were carried away to take of the fire, as it hath been signified:
2: And how that the prophet, having given them the law, charged them not to forget the commandments of the Lord, and that they should not err in their minds, when they see images of silver and gold, with their ornaments.
3: And with other such speeches exhorted he them, that the law should not depart from their hearts.
4: It was also contained in the same writing, that the prophet, being warned of God, commanded the tabernacle and the ark to go with him, as he went forth into the mountain, where Moses climbed up, and saw the heritage of God.
5: And when Jeremy came thither, he found an hollow cave, wherein he laid the tabernacle, and the ark, and the altar of incense, and so stopped the door.
6: And some of those that followed him came to mark the way, but they could not find it.
7: Which when Jeremy perceived, he blamed them, saying, As for that place, it shall be unknown until the time that God gather his people again together, and receive them unto mercy.
8: Then shall the Lord shew them these things, and the glory of the Lord shall appear, and the cloud also, as it was shewed under Moses, and as when Solomon desired that the place might be honourably sanctified.
9: It was also declared, that he being wise offered the sacrifice of dedication, and of the finishing of the temple.